Probability-A CLass 12 Exploration into the World of Uncertainty
Once upon a time in the city of Athens, there was a young mathematician named Anna. Anna was always fascinated by the chance of uncertainty and she knew that Probability was the only way to understand this. Wanting to share her knowledge with the world, she created a Probability Course.
This Course was open to all and it promised to make Probability easy to understand. As the students gathered, Anna began her class by rolling a dice. She asked her students the probability of getting 7 by rolling two dice.
Under Anna's guidance , the students learnt that there were multiple ways to get 7 by rolling two dice. As the course progressed, Anna introduced her students to conditional probability, independent events, Bayes Theorem and more. One of Anna's favourite parts of the course was when the students experimented with random events and realised how to distinguish between a random and Binomial variable.
By the end of the course, Anna had inspired her students to understand Probability, not as something to be feared, but to help them understand the world around them. And so, Probability, became a beloved course where students of all backgrounds came to learn, thanks to a mathematician named Anna.
How to study Probability for Class 12? You may have come across questions in Probability where each question follows a different approach. I am a mathematics teacher and coach, having taught Maths at the high school and college level for three decades and I can empower you with a good knowledge of Probability.
You need to have a basic knowledge of Probability, which you have learnt in Class 11. Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes. You learn the addition theorem of Probability.
A useful point to keep in mind while solving problems in Probability is to draw Venn diagrams depicting sets. You also need to know DeMorgan's laws. In this context, you will need to learn about complement of a set.
An Important point to note is that probability of any event cannot exceed one and cannot be negative.You would also need to have a knowledge of Permutations and Combinations while problem solving questions in Probability. Next, you will need to learn about Mutually exclusive and exhaustive events.
Two events are said to be independent if the occurrence of one event does not affect the other. In this context, you have the Multiplication Theorem on Probability. In this context, you'll learn about Conditional Probability.
You'll learn how to calculate the probability of a given event A given that event B has occurred P(A/B). There are a number of questions which can be asked in this context. You can refer to my links below to learn more.
That takes us to the law of Total Probability which holds for a number of mutually exclusive and exhaustive events and an event A which is associated with the sample space. Bayes Theorem is a beautiful application of this. Problems in Bayes theorem are easy to solve and all my students get it right.
Coming to random variables, a random variable is a variable whose values are determined by chance. You'll learn how to calculate the probability distribution of a random variable and how to calculate it's mean and variance. Note that mean is also called Expectation of the variable and variance is the square root of standard deviation.
Lastly, you have a Binomial distribution. This topic has been excluded from the syllabus for the year 2024. A Binomial experiment is any experiment that can be a sequence of n trials where
the trials are finite
The result of any trial is independent of the other trials. as, I tell my students, for a Binomial distribution, it is with replacement.
Each trial has only 2 possible outcomes, head and tail.